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doubly stochastic matrices forms a semigroup. So one can talk about irreducible elements, i call them primes. I am looking at the doubly stochastic matrices whose entries are rational. If i cleared out the denominators, these matrices will give rise to matrices with row and column sum constant, and i will take care that the gcd of all it's entries to be 1. The above problem with some more data counts how many 2*2 prime matrices are there with row and column sum $p^{\alpha}$.
